Title: A column generation on two-dimensional cutting stock problem with fixed-size usable leftover and multiple stock sizes

Authors: Supphakorn Sumetthapiwat; Boonyarit Intiyot; Chawalit Jeenanunta

Addresses: Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Thailand ' Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Thailand ' School of Management Technology, Sirindhorn International Institute of Technology (SIIT), Thammasat University, Thailand

Abstract: We investigate a two-dimensional two-stage cutting stock problem (2D-2CP) with multiple stock sizes when fixed-size usable leftovers are considered. A fixed-size usable leftover is an object with the predefined size that could be used later. Fixed-size usable leftovers can reduce the waste area and therefore can help construct better cutting patterns. A mathematical model is proposed in a set-partitioning form where the sub-problems corresponding to two-dimensional knapsack problem (2DKP) with fixed-size usable leftovers are generated for optimality testing. A column generation technique is applied in an attempt to find a solution that minimises a total waste. Moreover, two different practical integer solution finding strategies are proposed. The algorithms are tested on a real-world dataset using various initial solution patterns and analysed. Additionally, the effect of the usable leftovers is investigated when compared with the prior literature that used the same dataset on the 2D-2CP problem without considering usable leftovers.

Keywords: two-dimensional cut; cutting stock problem; CSP; column generation; usable leftover; guillotine cut; stock size; b&c; heuristics.

DOI: 10.1504/IJLSM.2020.104781

International Journal of Logistics Systems and Management, 2020 Vol.35 No.2, pp.273 - 288

Received: 12 Jan 2018
Accepted: 17 Jun 2018

Published online: 30 Jan 2020 *

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